Corpus ID: 218684701

The Rectangular Peg Problem

  title={The Rectangular Peg Problem},
  author={Joshua Evan Greene and Andrew Lobb},
  journal={arXiv: Geometric Topology},
  • Joshua Evan Greene, Andrew Lobb
  • Published 2020
  • Mathematics
  • arXiv: Geometric Topology
  • For every smooth Jordan curve $\gamma$ and rectangle $R$ in the Euclidean plane, we show that there exists a rectangle similar to $R$ whose vertices lie on $\gamma$. The proof relies on Shevchishin's theorem that the Klein bottle does not admit a smooth Lagrangian embedding in $\mathbb{C}^2$.